Deflection of beam in plastic range according to moment-curavutre properties of the section. 4

[3JC]

Dear collages of the forum,

As the subject says, I'm interesting into know bibligraphy about how to calculate on steel profiles the elastic-plastic deflection of a beam according to the moment-curvature properties of the section.

Thank you very much.

Regards,

Juan José

 

[GregLocock]

Should be in your structures textbook, if you've forgotten it. It was second year stuff for me, but then I'm a mechie, and didn't just have to look things up in tables.




Cheers

Greg Locock


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[civeng80]

Not a good idea to allow members to deflect in the plastic range.
Better only in the elastic range.
The use all the conventional methods of structural analysis and mechanics of solids.

 

[3JC]

Thank you very much for your responses. What I'm looking for is not the deflection on elastic range, but in plastic, and it is not a topic covered usually by classic texts. According to civeng80, my intention is not to do a design, is to study the hole moment-rotation curve to calculate the ductility of a steel connection, which behavior is similar to a beam.

Regards,

jJ

 

[GregLocock]

At any point along the beam the strain vs section height diagram is assumed to be linear. The bending stress is also linear until it reaches the plastic stress, at which point it becomes constant.

From that you work out the angle equivalent to that stress and the height at which it occurs along the beam, and hence the beams deflection.

Once the beam is fully plastic at some point then you have to have another think, and eventually you'll reach the fully plastic mechanism.

Despite what you say it is covered by classic texts, the first two I pulled off the shelves mention it at least in passing, and since it is easy to derive from first principles that is all that is needed.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376

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[rb1957]

research "cozzone"; but i'm confused, are you analyzing a beam or a connection ?

Quando Omni Flunkus Moritati

 

[3JC]

Dear rb1957,

Thank you very much. I'm analyzing a bolted connection, but I use a frame model approach to obtain analytical formulations. I'm going to see what you recomended and I will say something.

Regards,

jJ

 

[rb1957]

so the connection is going plastic ? that'll change the bolt loads (tending to reduce the plasticity in the connection).

isn't it "better" to have a connectin capable of carrying the loads elastically ? how big is this connection ?

Quando Omni Flunkus Moritati

 

[3JC]

Dear rb1957,

On construction applications, connections are calculated usually by the plastic resistance. You can see more information about this in the next link that I send in attach. In mechanical and aerospace engineering the problem is usually the high cycle fatigue; in structures submited to earthquakes, the designer has to garanty a good ductility of the connections against the low cycle fatigue (or so called plastic fatigue).

http://www.fgg.uni-lj.si/kmk/esdep/master/wg11/l0600.htm

Regards,

jJ

 

[BAretired]

To analyze elastic-plastic deformations of a section, you need to know the shape of the stress vs strain curve over the range of strain you are contemplating. Stress is usually assumed linear until first yield, then constant beyond yield strain but the stress beyond first yield varies considerably depending on the stress/strain curve of the material used. If the stress/strain curve is known, deflections may be predicted quite accurately using moment-curvature relationships.

BA

 

[3JC]

Dear BAretired,

Thank you for your response. On my particular case I have a multilinear stress-strain relationship for steel (linear, yielding, hardening and post-critic). Once I have obtained the moment-curvature for rectangular cross section (I have yet performed this task), could you recomend to me any text where explains how to obtain deflections, as you mentioned?

Regards,

jJ

 

[rb1957]

i think the OP is looking for more on "moment-curvature relationships"

Quando Omni Flunkus Moritati

 

[briancpotter]

Check out "The Plastic Methods of Structural Analysis", a classic textbook on plastic design. Chapter 5 gives an explanation/derivation of the moment curvature relationship for sections in plastic bending.

Brian C Potter, PE

http://simplesupports.wordpress.com

 

[3JC]

Dear briancpotter,

Thank you very much. Just I was cheking this text, and is very good on the topic (and also covers things that another not).

Regards,

jJ

 

[BAretired]

In the elastic range, curvature is represented as M/EI. Deflection can be found by using the ordinates of the M/EI curve and applying area-moment principles, the conjugate beam method or numerical methods such as Newmark's Numerical Procedures.

If the curvature is known at discrete points along a beam, whether in the elastic or plastic range, the same methods may be used because they are simply different ways of applying geometry.

BA

 

[wannabeSE]

3JC,
If you are interested in connections, have you looked at the Connections Conference Proceedings for the International Workshop on Connections in Steel Structures? There may be some articles of interest.

http://www.aisc.org/content.aspx?id=29480

 

[3JC]

Dear wannabeSE,

Thank you very much for the link. The propose of the study is for research (PhD), and therefore is more theoric.

Regards,

jJ